Econ 323 Hmwk 3

Assume that average product for six workers is fifteen. If the marginal product of the seventh worker is eighteen,

average product will rise between between six and seven workers.

Decreasing returns to scale" and "diminishing returns to a factor of production" are two phrases that mean the same thing.

False

The following production function satisfies increasing returns to scale: F(K,L)=10L+20K.

False

Suppose a production function has MRTS = K/(2L) with capital (K) on the vertical axis of the isoquant map. Suppose L=100 and K=400 at the current level of output. How much capital can be reduced if we increase labor by 1 unit to maintain the same output level?

2

A firm produces autos following the production function q =F(K,L)= 5KL, where q is the number of autos assembled in a day, K is the number of robots used on the assembly line (capital) and L is the number of workers hired per hour (labor). Then with K= 10 robots and L = 10, the maximum number of autos that can be produced is

500

When the quantity of variable input is 0,1,2, and 3, the total output level is 0, 100, 190, and 270 respectively. The marginal product of the third unit of variable input is _____.

80

When the quantity of variable input is 0,1,2, and 3, the total output level is 0, 100, 190, and 270 respectively. The average product of the first two units of variable input is _____.

95

Suppose capital is fixed and labor is the only variable input. When the output level is q=10, we know that MC(10)=4 and AVC(10)=7. It must be true that ____.

Average variable cost decreases at q=10.

Consider a firm with production function F(K, L)=3L+8K. Assume that capital is fixed at K=12. Assume also that the rental rate (price) of capital r=10 and the wage rate (price) of labor w=3. The cost of production is the total expenditure on capital (fixed cost) and labor (variable cost). Then the cost of producing q units is __? Hint: you need to compute first the total amount of labor necessary to produce q units of output.

C(q)=24+q

Assume that capital is fixed at K=1 and the rental rate (price) of capital is r=5. The amount of labor that is necessary to produce q unit of output is given by L(q)=q3/27 and the wage rate (price) of labor w=3. The cost of production is the total expenditure on capital (fixed cost) and labor (variable cost). Then the cost of producing q units is ___.

C(q)=5+(q3/9).

Consider a firm with production function F(K, L)=3L+8K. Assume that capital is fixed at K=12. Then, the amount of labor necessary to produce q units of output is ___.

L(q)= (q/3)-32

Consider a firm with production function F(K, L)=3L1/3K2/3. Assume that capital is fixed at K=1. Then, the amount of labor necessary to produce q units is _____.

L(q)=q3/27

Suppose isoquant curves are smooth and bend in towards the origin and the cost minimization point is determined by the tangent of the isocost lines and the isoquant. Except ____, all the other options characterize the cost minimization input bundle. (If a condition characterizes the cost minimization input bundle, the condition holds only at the cost minimization input bundle.)

MRTS = MPL /MPK

Ronny's Pizza House operates in the perfectly competitive local pizza market. If the price of cheese increases, what is the expected impact on Ronny's profit-maximizing output decision?

Output decreases because the marginal cost curve shifts upward

Suppose that a firm's cost function is given by: C(q)=1+3q2. Then, the expression for this firm's profit function is? (Assume the market is perfectly competitive)

Profit(q)=pq-1-3q2.

A firm's expansion path is:

a curve that shows the least-cost combination of inputs needed to produce each level of output for given input prices.

The short run is:

a time period in which at least one input is fixed.

Consider a production function F(K,L)= ALaKb, where A, a and b are positive constants. Then, F has increasing returns to scale if:

a+b>1

When marginal product of labor increases first and then decreases, the marginal product curve cuts average product from _____, at the _____ point of average product.

above, maximum

Bette's Breakfast, a perfectly competitive eatery, sells its "Breakfast Special" (the only item on the menu) for $5.00. The average variable cost is $3.95 per meal; the average fixed cost is $1.25 per meal. Bette should:

continue producing in the short run, but plan to go out of business in the long run.

At the profit-maximizing level of output q>0, which of the statement is wrong

marginal profit is maximized.

Suppose the isoquants are right angles and the kinks are on the K=2L line. The expansion path will:

follow K=2L.

Suppose isoquant curves are smooth and bend in towards the origin. When an isocost line is just tangent to an isoquant, we know that:

output is being produced at minimum cost.

The demand curve facing a perfectly competitive firm is

perfectly horizontal.

A firm produces autos following the production function q =F(K,L)= 5KL, where q is the number of autos assembled in a day, K is the number of robots used on the assembly line (capital) and L is the number of workers hired per hour (labor). If we use K = 10 robots and L = 10 workers in order to produce q = 450 autos per shift, then we know that production is:

technically feasible and inefficient.

When the price faced by a competitive firm was $5, the firm produced nothing in the short run. However, when the price rose to $10, the firm produced 100 tons of output. From this we can infer that:

the minimum value of the firm's average variable cost lies between $5 and $10.

When labor (L) is on the horizontal axis and capital (K) is on the vertical axis, which is NOT a correct definition/description of the marginal rate of technical substitution:

the ratio of the prices of the inputs.

When the marginal product drops to zero (and never goes up again),

total product is maximized.